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## Making a Box & Whiskers Plot

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**Making a Box & Whiskers Plot**Give Me Five!**5 Numbers are Needed**1) Lowest: Least number of the data set 2) Lower Quartile: The median of the lower half of the data set. (Also known as Quartile 1 or Q1) 3) Median: The middle number of the data set, when it is in order from least to greatest 4) Upper Quartile: The median of the higher half of the data set. (Also known as Quartile 3 or Q3) 5) Highest: Greatest number of the data set.**Least, Greatest & Median**When creating a box & whiskers plot, first order the data from least to greatest! 13, 5, 8, 7, 10, 6, 4 becomes… 4, 5, 6, 7, 8, 10, 13 Cross out the first and last numbers continually until you get to the middle number to find the median! Lowest Highest Median**Special Note About Median**If the data has two middle numbers, then place a line between the two middle numbers to represent the median. This will help visually find the Lower Quartile and Upper Quartile later. 4, 5, 6, 7, 8, 10, 12, 13 To find the median in this case, find the mean of the two middle numbers: 7 + 8 = 15 ÷ 2 = 7.5; The line in the middle will represent 7.5, the median. Median**Lower Quartile**Cover the median & only look at the numbers to the left. Find the median of the numbers to the left. 4, 5, 6, 7, 8, 10, 13 The median of 4, 5, 6 is 5. The Lower Quartile is 5.**Upper Quartile**Now, cover the median & only look at the numbers to the right. Find the median of the numbers to the right. 4, 5, 6, 7, 8, 10, 13 The median of 8, 10, and 13 is 10. The Upper Quartile is 10.**The Five Numbers**Lowest: 4 Lower Quartile: 5 Median: 7 Upper Quartile: 10 Highest: 13**Drawing a Box & Whiskers Plot**Draw an empty number line. Create equal intervals on the number line from the minimum to the maximum. (4, 5, 7, 10, 13) Place dots above each of the five numbers. Change the middle three dots into lines. Join the lines to make a box Join the box to the outside dots to make whiskers. lower quartile upper quartile median highest lowest 4 5 6 7 8 9 10 11 12 13**Interquartile Range (IQR)**The Interquartile Range is the difference between the first and third quartile. (Q3 - Q1) It teaches us about the majority of the data. On the box & whiskers plot, the interquartile range is the width of the box. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Interquartile range 10 – 5 = 5 IQR = 5